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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h2>Predictive variance example</h2>\n",
      "<p>In this example, we look at the predictive variance. Recall that, for maximum likelihood estimators\n",
      "$$ \\hat{\\mathbf{w}}  = \\left(\\mathbf{X}^T\\mathbf{X}\\right)\\mathbf{X}^T\\mathbf{t},~~\\hat{\\sigma^2} = \\frac{1}{N}\\left(\\mathbf{t} - \\mathbf{X}\\hat{\\mathbf{w}}\\right)^T\\left(\\mathbf{t} - \\mathbf{X}\\hat{\\mathbf{w}}\\right)$$\n",
      "we have mean prediction:\n",
      "$$ t_{new} = \\hat{\\mathbf{w}}^T\\mathbf{x}_{new}$$\n",
      "and variance:\n",
      "$$ \\mbox{var}(t_{new}) = \\hat{\\sigma^2}\\mathbf{x}_{new}^T\\left(\\mathbf{X}^T\\mathbf{X}\\right)\\mathbf{x}_{new}$$\n",
      "We'll start by generating some synthetic data from a third order polynomial with data between 0 and 2 missing:</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "N = 100\n",
      "x = np.sort((10*np.random.rand(N,1)-5),axis=0)\n",
      "t = 5*x**3 - x**2 + x\n",
      "noise_var = 300\n",
      "t = t + np.random.randn(N,1)*np.sqrt(noise_var)\n",
      "pos = ((x>0)*(x<2)).nonzero()[0]\n",
      "x = np.delete(x,pos)[:,None]\n",
      "t = np.delete(t,pos)[:,None]\n",
      "testx = np.linspace(-5,5,100)[:,None]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>Plot the data</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,t,'ko')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[<matplotlib.lines.Line2D at 0x104a0cd10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1049e72d0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>We now fit the models and plot predictive mean and variances (as error bars) based on the equations above. Note that the `diag` function lets us extract the diagonal of a matrix which allows us to compute the variances for all test points in one operation.</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "orders = np.arange(8)+1\n",
      "X = np.ones_like(x)\n",
      "testX = np.ones_like(testx)\n",
      "for i in orders:\n",
      "    X = np.hstack((X,x**i))\n",
      "    testX = np.hstack((testX,testx**i))\n",
      "    w = np.dot(np.linalg.inv(np.dot(X.T,X)),np.dot(X.T,t))\n",
      "    sig_sq = ((t-np.dot(X,w))**2).mean()\n",
      "    test_mean = np.dot(testX,w)\n",
      "    test_var = np.diag(sig_sq*np.dot(np.dot(testX,np.linalg.inv(np.dot(X.T,X))),testX.T))[:,None]\n",
      "    plt.figure()\n",
      "    plt.plot(x,t,'ko')\n",
      "    plt.errorbar(testx.flatten(),test_mean.flatten(),yerr=test_var.flatten())\n",
      "    plt.title(\"Order \" + str(i))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+Eg0SwWBsn1rvhSP+yyDVF0Cp96MMJseTFPXfTrYvne3hPi/br93e3u5OPmYz\nRsbPnmj7qxzoPzHZ9OnTnREjRiS9L/WlcliTcQ10/6pVjnPDDbZ97LGOc8st/v/MU203NTnOpZc6\nzpQpNuHclCl2u6nJJqUTGS73/+CAVL1DYVXQDO95EQKBxIFSgUCAnp5LCAQWJplYLKaqqorNmzcn\nve/AAw9k48bEKQwqKyvZvv1aHCec8fm//batF3vNNTBxIvzzP9tCJHv22P3+/syTV9PETzqnlp94\nTSWbaSr+oB8CkpU1ljNYfftAQd/KKecSCsUWu7ZyzIEHNA10/u+/byV0l1xiZXQXXAD33AO7d8PI\nkf7/zFUqKfmkkk1xJZ9eePABTQGmTt0vadCvrKx0O1mtCqeszBa7Hq5oZ+3kyXDaaba9fj2MHWtB\nf+TI4R8725SPl0KioF8Skk8vnEpVVRUzZ86ks3MuN91Ekjl0Krn22mszLnlcsSLWIfutb9n1a6/B\nQQdZq3ns2IwOnzXRTrpwODHQh8MK9OJ/CvoloYFAoP/0wskFWLCgpV9pY996+3B4eAF/7Vq4/37b\nvugiS+MAPP20BfqDDhrWYXOmb6s+mq5RsJdCoZw+pZDTT2cKhSpCoZlJZ5LM9LXfe88WCf/iF6G6\n2oL9XXd51yGb7c9cnbBSKJTTl72eeuqplAHfKnla9ubmvbBjBzz6qG1PnQqzZ9v2W2/B6NEW9L16\nrWxIlqdX+kaKgYJ+iUi1VmxVVZVnc9Ds2QNPPmnbkyfDccfZ9htvWCVLWZkFfL9SoJdSoKBfIlKt\nFTtz5syMO2RfecWuA4FY5+uzz8Jhh1mgj5Yu+o06ZKUUKegXiFTz4vR5FDNmzGft2rWAw4wZtqgJ\n1KVYK3b4y/+9844NnAI4010y9pe/tDliRoywgO9n6pAVGbrvYEscPg/8LzA+7r552Dy2rwCz4/af\nBPzRva9lgGPneOhy/+1k+9LZHu7zBjpGe3u7EwgEHIif6iCQMNWBTatQ0+cxODU1NQ7Y4+wxIScY\nDDqhUGjv/nTP//33HWfhQtseP95x5syx7d27s/O+vX5eU5NdgsHYtqY9kGLi/r8fUCZdaecAv8HW\nl7vV3Xc9cAxwP3AyMBl4HDjSPZnlwNXu9aNAK5BsSI97/rnh9+qdgZYe7OjoGPAx7iNxnI5hvfau\nXfDEExAKwfjx8NGPwmOP2cjZffYphKol21bljZSCbFfvLI7bfhr4tLt9AfAAsAtbqmgNcArwBjAO\nC/gA9wLY7BYaAAAPMUlEQVQXkjzoS5xUnbDxC4ykeoz7yCG9nuPAc8/Z9mGHxVYSevVVOPhgC6b7\n7DOkQ+aUOmRFUvMqp38FFugBJgHL4u5bh7X4d7nbUevd/TKIVJ2wFRUVe3P9L7zwwgBHSG+a4z//\n2a6POw7+/nfbfuIJW1O0rMwCvl8p0IukZ7CgvxioSbL/BuDX7vY3gZ1YSscz4bhVCGpra6kt4f+9\nqTphZ82atXcO/BRzorkLlafurN2yxQZOAUyfbtc/+hF87GPWIXvUUZ68Bc+p8kYEurq66Ir+Z8iR\ny4Dfk9iUvN69RHVg6Z0arOM36mLgrhTHzXHnR/9tP3TkWsfrbCcYDDrTp093YEZCJ6zNg99/Pvvy\n8nIHqpwZM2bsnTc//jV27HCchx+27f32c5xPfcq2e3v98b6Hsy0i6XXkZpLeORf4BhAkMWn8CNbq\n/w8sfXMklsd3gG3YF8ByYA7WkStJhMM2bQJsj1vJKsA3vnHj3nlxduz4TtLnfuxjH6O7u4sVK2L7\nHCc2cGrSJDj2WNteuxaqqix9kyKL5DvxqRytSiQyNJkE/TZgNLEO3aeALwOrgAfd693uvui3z5eB\nnwKVWPWOOnGTiqSYJ6eHtra2vYOpBsr1R0VXOgwEILp7xQpbVLuszAJ+IVDOXsQbmQT9Iwe479vu\npa8VwPEZvGaJaE05T058xU6yXH8gEGDOnK/R2Qknnwzr3K7zX/wCTjzR8vRTpmT15D2jQC/iPY3I\n9aXU5Zfxrfhoi7++vo3TTnP43e/OYMKEK/jKV2x+4ptvttGyo0bFOmn9ToFeJLsU9H0pVXK9MmHa\nhA8+gNGj64A6XnzR9l1zjS3Nt+++sZktC0lc0ZaIZIGCvi+dSmXl0oQUT3TB8fPOq0sYODVpkm2/\n/LItHv75z+fhdDPQt/RSHbMi2aWg7wORSITW1lZgBzNmbAPe7hfwr7rq37nzzq9y/PE2BQLA44/D\n0Udbh2xNstEUPqdJz0Ryz6/LWLglp7mR37l3IgQCfdegjRqPzW5xCaNGzWDXrvEsXWrz34wcmZt5\nf3Ix55CIeCOduXcU9Ml38AsB8ROljcKGQMzBJij9DbCAj3/8fZYuXZzzyd68fp4mQBPJHi2XWBCi\nlTqnApcAF2EDlxcCXwS2ADB2bCgfJ+cJVeSI+IeCfh699hrAlcB/Y9MXLcRmpH4j4XGBgC120tmZ\n6zP0hipyRPxDQT+HIpEI11//XeBkyssvoqxsKhDgkEO+yrp1j8Q9soYZMyYxbtw4ursraGmZm/GS\nhrmmqRJE/Ek5fbKf2/7732GffZ5lzJhN7NhxMhABFmDryxxIU9NVLFu2jM7OXkKhCjo75+I4dZ68\ndq6OoXy9SP6pIzdN2Qj6H3wA5eVw6aXwq1/Bli0rgDuBXwJ/S3j9+BWw8lVB4+Vri0h+pBP0R+Tm\nVEpDNOh94xuxhcFPPBHa2h4HzsZy9n/r97z4+XQKSbKBVeFwbL+I+I9y+h548027PuEEux49GhYv\ntumLt2wJc8MNNkVyKvHz6RQKDawSKUxK7zC8NMfWrTBhApxxBjz/PLz3Hvz2t3D66YkDryorL0o5\nY6apob397r1z5BdaekdE/EM5/TSlG/x27rSFRi66CDo7Yds2m7L4vPOgsjLZ8/oOvIoZOXIk06ZN\n49lnb+zXaevXoK+OWhF/0+AsD0SD3le+Ag8+aNtnnQV33QXV1fCpTw307NRTJJ999tl7O2/9TAOr\nRIqLF0H/a8B3gAOA99x984ArgA+ABmLN3ZOwlbMqsJWzGj14/awJh2HhQtueOBGWL4cjjoCrrkr3\nCOlNkexnGlglUlwyDfqHAueQOIT0GOCz7vVkrBj9SMABfgh8AVsj91FskhnfLJn47rt2PWuWXW/e\nDD/7ma1A9W//NpwjNhAIJK5sFZ0i2c+DrTSwSqR4ZZpc+B/gJuBXWCv+PayVvwe4zX1MBxDGvhie\nAI52938OqAX+Jclxc5bT374dxo6F+npYutQ6aB97DD7xCW9y4u3tEdra2vYOvJo7dy719XV5nfRM\n9fYixSnbOf0LgHXAC332TwKWxd1eh7X4d7nbUevd/Xl1wQV2/ZnPwAMPwLhxcO653h2/rq5ub2VO\nh29+0yTSQiYipWOwoL8YSLY8xzexFn38gnyedkmG45LJtbW11GYp+kQiVlc/Z05WDu97qrcXKVxd\nXV10DXE05HAD9XHYRO9/d28fgrXcTwEud/fd6l53AE1YemcJsfTOxUCQPKd3IPNUSSQSob6+lWBw\nB93dY2hvb0iou0/nGMN9bS+eJyLFIZvpnReBg+Nu/4lYTv8R4H7gP7D0zZFYx60DbMO+GJZjq4S0\nDvP1fSMSidDY2Aj00N1t+xobox23/uysVUetSOnyKiXzOvARYiWbN2Alm7uxsszoTPDRks1KrHqn\nIcXxCqalP3t2iEWL+g/ACoVCdHZ2+LqlLyLFJZeDs47oc/vb7qWvFcDxHr2mL+zYkXwAlt8mUVPr\nXkRAI3IzNmZM8gFYfptETYOsRAQU9DPW0NBAT0/iACy/LG+o1r2I9KWgn6HoyNr6+jaCwd68L2+o\nuXJEZCB+ne6rYDpy/TC9sUbTigholk3PRSIRoJXa2h1uLr+BfJdlajStiAyFWvqkP4dOY2NjQu4e\nArS3t3iyAMpAr60yTBFJhxZRSVM6gTdVPX51dTX33HPP3knUchn0taiJiMRTesdDqerxN23a5I7I\nhVynelSGKSJDpaCfplT1+ICb8mkjF0FfZZgikgkF/TSdeuqpLF26dIBFznMzAletexHJhIJ+WiIs\nXLhwgIAPtgJkdqh1LyJeUUcuqTtT29sjtLa2smjRM8DmlM8PBAL09LTgOMOfTrnva6syR0SGStU7\naUoeeCMEAn1LNPsaTyg0K2EJRK+CvipzRGSoFPTTlHwxlBeBTYM8M4TjdCQcQ+vUiki+qGRzCJIt\nhjIQS+nM9ez1NbJWRHJBLX0GHnzVXxWh0MyElE70GF619EVEhiMXLf25wJeBD4AIcJ27fx62ctYH\n2AQ10WgaXTmrAls5qxGfSDX4Kl60w7ajw9t6fFXniEiuZBL0zwDOB04AdgEHuvuPAT7rXk8GHsfW\nyXWAHwJfwNbIfRQ4F1s4Pe9SDb6qrq5m06bjCIUq9rbuvabaexHJlUyC/peAW7CAD7DRvb4AeMDd\nvxZYgy2G/gYwDgv4APcCF+KLoB9hzZo1/faWl5dz9dVX09wcpsPjs1TrXkTyIZOgfyRwOrYWbi/w\ndeAPwCRgWdzj1mEt/l3udtR6d39e2XTJV/L66xv63bd7926WLVvW/0keUOteRPJhsKC/GKhJsv+b\n7nOrgFnAycCD9F8gfdjCcVGxtraW2iw1gefPnw/0D/hRXi5wrta9iHipq6uLrmjpX5oyqd55DLgV\niBY4rsG+AK50b9/qXncATVh6ZwlwtLv/YiAI/EuSY+eseqeqqootW7akvD8UCtHZ2eHptMgiItmQ\nTvXOiAyO/zBwprv9YWA08C7wCPA59/bhWBpoOdac3obl98uAOe4x8sr9kJKKLnAuIlIsMsnp/9i9\n/BHYCfw/d/8qLNWzCtiNlXRG27hfxko2K7Hqnbx34k6dOpXNm5PNqzOOlpaWjBc4V0pHRPyk5Adn\n2dQLVxKf16+pqWHDhrtxHAv4mixNRAqB5t5JU1lZhFCojd7eXrq7K2hvTz7aNp1tTZYmIvmioJ8m\nLxcnV+teRPJFE67liCZLE5FCoZY+3rb0RUTyRemdNGUS9JW/FxG/UNBPkxctfRGRfFPQT9NQg75a\n9yLiRwr6adJ0CiJSDLI9DYOIiBQYtfRJr6WvlI6I+J3SO2nSdAoiUgwU9NOk6RREpBgo6KdJ0ymI\nSDHQNAxDpOkURKTYqaWP8vciUhyyXbI5E1sRayXwDLZObtQ8YDXwCjA7bv9J2KIrq4GWDF5bRESG\nIZOgfzswH5gOfMu9DXAM8Fn3+lzgB8S+eX4IfAFbQvFI935fCIcT0zrhcCzd47WhLmRcSIr5vYHe\nX6Er9veXjkyC/tvAeHd7ArDe3b4AeADYBazFFkw/BZgIjMN+HQDcC1yYwet7Kj7QR7ezlccv5j+8\nYn5voPdX6Ir9/aUjk47c64HfAXdgXx6nuvsnAcviHrcOmIx9CayL27/e3Z8XXV2xlrw6bUWkVAwW\n9BcDNUn2fxNocC+/BC7CFkk/x9OzyyIFdxEpRZlU72wD9os7zhYs3XO9u+9W97oDaALeAJYAR7v7\nLwaCwL8kOfYaIJDBuYmIlKIe4EPZOvizWNAGOAur4AHrwH0OGA0c7p5E9MvlaSy/XwY8io86ckVE\nZGAfwYL4c8BTWBVP1A1Ya/0VIBS3P1qyuQZozc1pioiIiIiIr8wFXgZeBG7L87lky9eAPcD++T4R\nj30H+7d7HvhfYqW9he5c7NfrauC6PJ+L1w7F+txewv7PNeT3dLJiJDaY9Nf5PpEsmAA8hP2/WwXM\nyu/pDN0ZWOXQKPf2gXk8l2w5FOvk/hPFF/TPITYG5FZinfqFbCSWlpyK/V0+R6wooRjUACe62/sC\nr1Jc7w/gq8B9wCP5PpEsuAe4wt0upwAbWg8CZ+b7JLLsf4ATKM6gH+8fgYX5PgkPnIp9SUddT6xS\nrRg9jBVoFItDgMexBmWxtfTHA6+n+2C/Lpd4JHA6NsirC+s0LiYXYAPVXsj3ieTAFVilVqGbDLwZ\ndzs66LAYTcUKM57O83l46T+Bb2Dp1GJzOLAR+AlWVfn/gbGpHpzPqZUHGvhVDlRheamTsZb/Ebk7\nNU8M9P7mkTgRnV9nOx1Iqvd3A7GW1DeBncD9uTqpLCqVuVf3xXLDjcD7eT4Xr9QDf8Hy+bX5PZWs\nKAdmAFdjpfN3Yr9Cv5XPkxqqx4iNAQDLpVbn6Vy8dhzwDpbW+ROxOYoOyuM5ZcNlwO+Bijyfh1dm\nkZjemUfxdeaOAjqBf833iXjs29ivtD9hc4b9DZv7q1jUYO8t6jSgPU/nMmxXAc3u9oeBP+fxXLKt\nGHP652JVIAfk+0Q8VI4NNJyKDTwsto7cMiwQ/me+TyTLghRfTh/gt1isBAhTgBWPo4AF2ECuFRTn\nT7Ko1ym+oL8am3ZjpXv5QX5PxzOfwKpa1mAt/WJyGpbvfo7Yv1sxjpgPUpzVO9Ow1E6xlUmLiIiI\niIiIiIiIiIiIiIiIiIiIiIiIiIiIiPjD/wFk5aH8Tc1eLwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105089390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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E58rh/YEzgH8BDgMeA/7KN7+5jSeeuL8o0iXFvO1CvcG7FI9CTxMpGCSQ7QNM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\nREREREREsun/A1vdeovQ4g/AAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10505be50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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emwlcBxzCFnXx5xXOARYBqVit4LQW3ls5/SAtLaNQWFjIjBnFeL3w1luf8eqr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\niIiIiIiIiIiIiEjn8L8SH6EliwjvwAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104eb0c50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7fr/G25P6DXASeC5UjWpDsbJpcxdMbng68HWY2xIs44EDmHy+M7xN\naRPxQBZwF6Z0/mHMX6G/DWejztSbeOcAgMml9gpTW4JtOLAfk9b5DO8aReeEsU1t4RbgfSAxzO0I\nltE0TO/MIvoGczsCbwF3h7shQfYHzF9pn2HWDDuOWfsrWqRivpvt28DKMLXlrN0BzLWOhwCfh7Et\nbS0ac/pjMVUgvcPdkCCKx0w0zMBMPIy2gVwHJhA+FO6GtLEcoi+nD/AeJlYCuIjAiseOwDLMRK6P\niM4/yWy7iL6gvwOz7EaRdXs0vM0JmmswVS07MT39aPJtTL57A97/3aJxxnwO0Vm9MwKT2om2MmkR\nERERERERERERERERERERERERERERERERkfbh/wNp9PNPUX+DpAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105127ed0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ruvr8/HxKSubHoJUiEm1K7ySR0FUe/X446SR48knYvh2GDPk/qqvXt34F2dnv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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105068710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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W9jIAG+T+gOQL+l8mNAfkXkKD+h1ZGpaWHIj9d/kOoaKEZJADnO8c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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104ccc150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9QuypnrS0TAoKhlJUVMS//3uheo8iCUhBXwAz4Dd06Nfs3LmMr79+CrOatq2x\nY/eyatWc6DdORCJGA7kppn3v/vzz4e23zf0BA+ZRVXWvdeX/tXme0+lkxoy5UWqliMSSgn4SsQ/q\nORxmA+2AXbsGY1bU2vnJzf2g08JjIpJ8FPQTXKj54JWV5r7LBb/4BfTuDSefvJDNmzvO1S8q8ijg\ni6QQBf0E0VkZhfa9e6dzLS++mAcs5Pnnj+bTT8/G5Spk4MBScnPLqKt7hcAiq+5UsRSR5KKgnwA6\nK6MAtPbS9+4F+JA//KGZlpbRwOdUVoLDEZyC6fNtoLQ0k8ZGl6ZeiqSocGbvPARMAPZh9r27Cdhl\nPTYduBk4AJQAgbzCmZi6vJmYIuzti7oEaPaOTegyCi6czluYNGkSS5fC+vUN1NRUYzYzqWhzpWbm\niKSGnp69sxS4G7OzxgOYQD8NGAl83/o5BHgDGIEp5vIEpij7KkzQvxRIzvq7EdS2jEJAOUOHwtVX\nT2LmTHA6F1FTc2PI5/ft6wp5XkRSTzhB/3Xb8UrgKut4Imblz37MZqcbMWv8N2M2UV1lXfc8cAUK\n+oeUkZFhHbWtY79hw79xtlU9YejQ37epdmmXmZnZk80TkQQSqZz+zZhADzAYWGF7rArT499vHQds\ntc7LIQS3BCwnWOnyJ+zZ4+Laaz/mmWf+xcqVl9G23r0fKG8tjCYiAocO+q8DeSHO30Nwhc+9mLz+\nggi2q00xL7fbjTuF6wIEBlsD9W+++uoKPv74VmbOXEVp6U1ABY2NHZ+XarXtRVKN3+8/7G1Jwy3D\nMBn4EXAhEAg706yfD1g/yzCrgjZjtlk61Tp/LSZfcWuI19VALrTuarVjx2mkpaXRt+/ZDB1ayPLl\nsGsXnHTSfCor2+d0zIKroqIizc4RSTE9PZB7KXAnJnDb+5mvYnr9j2DSNyMwefwWoB6T318FXA/M\nC+P3JzWv18ucOXNoaGiwnZ3NV18V8/772RQUwLBhz1BZWd7huaNGuZJ2f1oRCU+vQ1/SqVLgKEwK\naA3wuHV+LfCS9fOvwG0EtmEyx08DGzADvIpMIfh8vhABfxpwJSef/GPy882Z4ABvWxq4FZHOqMpm\nHOq46ck5wFnAXPLzT2Ly5Mn4/TB48HrKyjquslUtHZHUpCqbCSo7ezXBWTo/BYYDZwBbOeUUD17v\nZOuxQq2yFZHDop5+HAquwL0ZuB/4E7AThyOdH/zgGgoLC7VNnoh0oJ5+ArFXy9y2rZTs7A3s2XM+\nZnLTAts6CasVAAAMlElEQVS+tIWxa6SIJDz19OOQw7GC3r0Lycr6Lrt3v8+YMSfxq1/9SmkbEemS\nevoJwl42ubo6D/gdzc3/w+7dbsDNZ58N4I9/HEF2tlI6IhIeBf0Ymz17OQ89VEFd3TlAP0w9ujJM\nMVIzmFtXB7W1HtxuzXAVkfAo6MeY3++lrm4pcDSmLLIXeLTDdY2h6iyIiBwmBf0YM2WTewNvAnsx\nwd++l60fKNeCKxGJCAX9GLDP1HnvvSnAw5iq07diyhO1pW0NRSRSFPSjKNQ+t7t2jSE9PZ39+88C\ndgOQl5fH4MGDycnJ0YIrEYkoBf0oCbXPrd/fB1jAE0+sZtGif2PJkkY8HgV5Eek5mqcfJR3r6QzA\nzNR5jmuvvYjCwkL8/uCUTK24FZHDpXn6caRtPZ1sYDmmMvUT1NZ68Ho1HVNEel44pZWlm3w+Hx99\n9JHtzDPAasw+8ZqOKSLRo6Dfw7xeL9dccw01NTXWmTswFTO3YaZmzqCq6ha83uCMHhGRnqL0Tg+a\nPXs599+fTnPzXdaZfOAaTPXMRYC9/n2MGikiKUVBvwf5/V6am5da944F3gWuBpbQr18/xo0bp5k6\nIhJVCvo9yKy2BZNFWwD8AVgCwLhx47SPrYhEnYJ+hNlX277//hTAbd0GAweBGTgc6QwYcA1er6Zm\nikh0RWKe/h3AQ8AgoNY6Nx2TuD4AlACBHMeZmPKRmcBrwNROXjMp5uk7HD4GD17Itm1zgDHAdttm\nKN4Yt05Ekk135umHO3tnGHAxsNl2biTwfevnpcDjtkY8gVmRNMK6XRrm749z42lqeoozz3wMOAWP\nx8OiRYsU8EUkZsJN7zwC3AX8r+3cRGAhsB/YBGwEzsZ8MOQAq6zrngeuwBSPTzqBLyq33JLFAw/8\nBocDlMIXkVgLJ+hPBKqAD9qdHwyssN2vAoZgPgSqbOe3WucTnj2PHyilsML6C6Sng9cLLpf5Ccrj\ni0jsHCrovw7khTh/LyZvf4ntXETr+NhTIG63G3ccR0l7EHc4YN48+O//NvdnzYpVq0Qk2fn9fvyH\nuarzSAP16cDfMLt+AAzF9NzPBm6yzj1g/SzDLD3djCkWf6p1/lrAhSki315CDeTaSyaXl+dwwgkL\n+NWvcpg8OZjmERHpaT1ZcO0j4Djb/c8wM3NqgVcxk9IfwaRvRmDy+C1APeaDYRVwPTDvCH9/3OhY\nMnkutbXlDBzoALToSkTiS6RSMpXAWQSnbN6DmbLZjJmWucQ6H5iymYWZslnSyeslRE/f74cpU+ZT\nWRkI+E7gSuBVnM6DDB06SaWSRSRqutPTVz39MLndbsrLy4FczJj2jcCbuFyuw861iYiEIxrz9FNe\nRkaGdfQ48DJmg3O0kbmIxCUF/TCVlJRw7LFTgVGYCU3ayFxE4pfSO2Hatg1OO62JnTvvwOX6iPLy\nTBYvVuVMEYk+bZfYA+wLsZYtgy++gPz8DHbufKx1oHb1anPT4K2IxBv19MPgcMA3vwkrV0JGhubk\ni0hsqacfYfZFWAcPDgWe4fnnM+jTJ9YtExHpHgX9buq4CGsJ8Biff34K3/iG8vcikhiU3umGjouw\nxmDWoj2M0zmGSZMmtRZaA+XyRSQ2lN6JELcbhg17hsrKckxliTXAt4GPqK3NZezYXLxe9fZFJP5p\nnn43BRdhPQmUYsoPQV1dHVOnTsXn88WqaSIi3aag300lJSUcc8zPgeOB2W0eq6iooLS0NCbtEhE5\nHCmb3gm18QkE8/HtH8/NPYWamm9jyi3c2+H1qqt39mRzRUQiQgO5mPn2Xf06h8NHdnYae/a8C/wi\n5DUej4cy7YcoIjGkgmth8vl8eDwe4CX27MkHQm+DpVo7IpIoUja9cyjBefm1mEHbq4GmNtf069eP\ncePGUVysWjsikhiU3sGkd2bMgLff3sI//lFLZmYL9fV7aGnZAJwB7CZQMtlu7Ni9rFo1J2rtFBHp\niubpH4axY3288MJUmpoqaGrt0F8MuIHzgD1trnc6ncyYMTeqbRQRCZd6+pie/iWXeFi6dKntbDbw\nIWbf9uD53NxcioqKlNIRkbgTjYHcYuATTNL7Qdv56cAGYB1wie38mZhIugGIq25yU1NTuzOzgLex\nB3yn08n8+fMpKytTwBeRhBROeucC4HLMllH7gWOs8yOB71s/hwBvACOAFuAJYAqwCrMx+qVAXMxz\nDK64BSjC7HX7FFlZD9Knz7EMGtSboqIisrMLY9RCEZHwhRP0f4JZmrrfur/D+jkRWGid3wRsBM4G\nNgM5mIAP8DxwBXES9EtKSvjggw+orq4BngZuIy+vnKefflq9ehFJGuGkd0YA5wMrAD+m7CTAYKDK\ndl0Vpsff/vxW63wc8HHfffdRU1MDTMN8Pr0Y4zaJiETeoXr6rwN5Ic7faz03FxgHjAVeAk6KaOui\nwBRKu4U1a6qBU4ESYDQA1dXVlJaWqqcvIknjUEH/4i4e+wnwinW8GjgIDML04IfZrhuK6eFvtY7t\n57d29uJer7f12O124+6hAvX33XcfUI0Z8H4KmIH9C0ljY2OP/F4RkXD5/X78gSJh3RTOlM0fY1I2\nM4BCzIDtCZgB3AWY0dDAQO5wzEDuSkxXehXgA+YROqcftSmbubm57Ny5E/gPzFt6xWqq4XQO5+mn\nJ2lTFBGJez29OOv31u1DYB9wg3V+LSbVsxZoBm4jGEVvA54FsjCzd2I+iGv+SMMAL3Au8GnrY06n\nk7lz5yrgi0jSSPnFWaNHj+G9934N/BO4v/V8Tk4OCxcuVD5fRBKGqmx2w4UXPgMUAMEaOnl5eQr4\nIpKUUr72zldfjQb+jsfzbRobGykvz+Tpp1ViQUSSU8qnd6DtJiqH2lBFRCReKb0jIiJtKOiLiKQQ\npXcIbqICoTdJFxFJBN1J7yjoozy+iCQH5fRFRKQNBX0RkRSioC8ikkIU9EVEUoiCvohIClHQFxFJ\nIQr6IiIpREFfRCSFKOiLiKQQBX0RkRSioC8ikkIU9EVEUkg4BdeKgMeAdIIboK+2HpsO3AwcAEqA\npdb5MzEbo2diNkaf2slr93jBNb/f3ALHqqwpIomuOwXXwuEHPNbxZcAy63gk8B7mw6AA2GhrxCrM\nhwWYoH9pJ6/dksyWLVsW6yb0mGR+by0ten+JLtnfH3DI3nI46Z0vgH7WcX9gq3U8EVgI7Ac2YYL+\n2cDxQA4m8AM8D1wRxu9PWP7AV4wklMzvDfT+El2yv7/uCGdj9GnA34GHMR8e51jnBwMrbNdVAUMw\nHwJVtvNbrfMiIhIlhwr6rwN5Ic7fi8nVlwD/A1wD/B64OKKtExGRiAon4V8PHG17nZ2YdM8069wD\n1s8yYAawGZP3P9U6fy3gAm4N8dobAWcYbRMRSUUVwPCeevF/YYI2wIUEZ+4EBnL7ACdajQh8uKzE\n5PcddD2QKyIiceYsTBB/D1gOjLY9dg+mt76O4AwfMFM2P7QemxedZoqIiIiISFwpBj4BPgIejHFb\nesodwEFgQKwbEmEPYf7bvQ+8QnBqb6K7FPPtdQNwd4zbEmnDMGNuH2P+nyuJbXN6RBqwBvi/WDek\nB/QHXsb8f7cWGBfb5hy+CzAzh9Kt+8fEsC09ZRhmkPszki/oX0xwDcgDBAf1E1kaJi1ZgPl3+R7B\nSQnJIA/4pnV8FPApyfX+AP4T+CPwaqwb0gOew1RBADMrM+E6Wi8B3451I3rYImAUyRn07a4EXoh1\nIyLgHMyHdMA0gjPVktFfMBM0ksVQ4A1MhzLZevr9gMruXhyvBddGAOdjFnn5MYPGyWQiZqHaB7Fu\nSBTcjJmpleiGAFts9wOLDpNRAWZixsoYtyOSHgXuxKRTk82JwA7gD5hZlU8BfTu7OJwVueHqauFX\nbyAXk5cai+n5nxS9pkVEV+9vOnCJ7VyPFUjqQZ29v3sI9qTuBfYBC6LVqB7UsxUA48dRmNzwVODr\nGLclUiYAX2Ly+e7YNqVH9AbGAD/FTJ3/L8y30F/GslGH668E1wCAyaUOjFFbIu10YDsmrfMZwRpF\nx8awTT1hMvAPTEXVZDCOtumd6STfYG46sAS4PdYNibDfYL6lfYapGbYHU/srWeRh3lvAucDiGLXl\niP0YmGkdFwKfx7AtPS0Zc/qXYmaBDIp1QyKoN2ahYQFm4WGyDeQ6MIHw0Vg3pIe5SL6cPsBbmFgJ\n4CUBZzymA/MxC7neJTm/kgVUknxBfwOm7MYa6/Z4bJsTMZdhZrVsxPT0k8m5mHz3ewT/uyXjinkX\nyTl75wxMaifZpkmLiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiMSH/w+w3XPWuHgdHgAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104f815d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qBp1crNrAn/5kr2fMgJtugl27rgA+F/1OSkpyFAhEOhEFgzTX2gxiiOws9Hiq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\nCw9GAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104b038d0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>We notice that the variance decreases but then starts increasing again as the model order increases. This is due to the increased flexibility of the higher order models, particularly in regions where there is no data. The following plots show possible models - as the order increases it's clear that the models exhibit greater variability within the areas lacking data.<p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "orders = np.arange(8)+1\n",
      "X = np.ones_like(x)\n",
      "testX = np.ones_like(testx)\n",
      "for i in orders:\n",
      "    X = np.hstack((X,x**i))\n",
      "    testX = np.hstack((testX,testx**i))\n",
      "    w = np.dot(np.linalg.inv(np.dot(X.T,X)),np.dot(X.T,t))\n",
      "    sig_sq = ((t-np.dot(X,w))**2).mean()\n",
      "    testmean = np.dot(testX,w)\n",
      "    covw = sig_sq*np.linalg.inv(np.dot(X.T,X))\n",
      "    sampw = np.random.multivariate_normal(w.flatten(),covw,10)\n",
      "    plt.figure()\n",
      "    plt.plot(x,t,'ko')\n",
      "    plt.plot(testx,np.dot(testX,sampw.T),'r')\n",
      "    plt.xlim([-1,3])\n",
      "    plt.ylim([-100,200])\n",
      "    plt.title('Order ' + str(i))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KURw/zpWDh4fI4sXJul0lYwI1BIrylFy4wHTPl14yNWpJjLkUtK10T3MOHRKp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\nhBBCiBT5DwkJrGU2Kh2wAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104ce1bd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bUgfIGSYTx+TnR8E467f8LVvYDL5mTWYFTZ1qu0ow6h0qV2adgtFn2M8v44wl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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1049f9450>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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boS9YYKadbt3smrIyE9hpaVZzZ8gQq8p50kkwbpxl3DZmb1+zxvwEb75p+QEr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\nCV988cWu1zIXCSE6K0npLG4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       "text": [
        "<matplotlib.figure.Figure at 0x104d99110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x104db5d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vvlmp6Gil3niD360u2GxKzZmjVOfOSv3nP8wY9hHggVFDjcH+nQRBOC1lZVx8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\nBEEQBEHwRP4/QFQcsDk4xdsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104b51f50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xpk3O3XSTc+3aOffssxYNdIRgisAwjDKsXKkEq86dnRs40Lm//EUzgsOxZYtz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\nDMMwDMMwDMMwDMMwIpH/B6BP1OM+QaQ3AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104b05d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OscLn22/zfUAAncb799NsdOoUbfUzZzJpyzprNz6eu319/TUwZQqriHbvbv97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\n4K4t6hWfAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104d12210>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KRikXVQSK0lApLGQhNkPw//47heuoUVQAbm6cLRvCPzeXQt8Q/t27V0zwAyzP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\n21P4T5pUfkG3S5e4evvsMyq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ZZdOmNB+0bGlJamrWjM3f33JsNB8f4PJl3HfTTTi5bRsC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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104cd3050>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}